Is it normal for my bilge pump to cycle on and off every few minutes?

[MiLoII]

As others have indicated there are auto sensing pumps that have no float switch. They activate momentarily at regular intervals. If they don't sense any water they turn off immediately. If they do sense water they continue to run until the water is pumped out. I went thru 2 of those in the bilge under the stairs before I gave up and went back to regular old fashioned float switch activated pump and very happy with that 3 seasons later.

 

[GypsmJim]

Replace that sucker with a pump with a float switch. There should be a 2 position switch - on and auto. Yours is a stupid idea that will eventually drain your battery.